Method and Apparatus for Partially Desalinating Produced Water to Form Extraction Fluid Used for Fossil Fuel Extraction

ABSTRACT

A method reuses produced water resulting from a fossil fuel extraction operation. The method includes providing the produced water as an input to an electrodialysis system. The method also includes running the electrodialysis system to produce a diluate and a concentrate. The diluate is contaminated so as to have a conductivity of no less than 0.1 Siemens/meter. The method also includes reformulating the diluate to produce fossil fuel extraction fluid. The method also includes using the produced fossil fuel extraction fluid in the fossil fuel extraction operation. An electrodialysis system includes first and second stacks. The electrodialysis system also includes first and second voltage sources, coupled to the first and second stacks, so as to apply a first voltage to the first stack lower by at least about 10% than a second voltage to the second stack.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationNo. 61/982,973, entitled “System for the Desalination of High SalinityWaters” and filed Apr. 23, 2014, which is hereby incorporated byreference herein in its entirety.

TECHNICAL FIELD

The present disclosure relates to reusing produced water collected fromfossil fuel extraction operations, and more particularly, to runningelectrodialysis systems at low voltages to partially desalinate theproduced water. The resulting diluate from the electrodialysis systemscan be used in forming fossil fuel extraction fluid.

BACKGROUND ART

Fossil fuel extraction systems produce extraction fluid by combining atleast fresh water with viscosity modifiers. An extraction system injectsthis fluid into a well. Subsequent to injection, a fluid containing atleast fresh water returns to the surface as produced water. The systemcollects the produced water, recycles the water via distillation, andcombines the distilled water with fresh water and viscosity modifiers toform more extraction fluid. Distillation yields water of high purity,but also adds substantial costs to the extraction system.

SUMMARY OF THE EMBODIMENTS

In accordance with one embodiment of the present disclosure, a methodreuses produced water resulting from a fossil fuel extraction operation.The method includes providing the produced water as an input to anelectrodialysis system. The method also includes running theelectrodialysis system to produce a diluate and a concentrate. Thediluate is contaminated so as to have a conductivity of no less than 0.1Siemens/meter. The method also includes reformulating the diluate toproduce fossil fuel extraction fluid. The method also includes using theproduced fossil fuel extraction fluid in the fossil fuel extractionoperation.

In various embodiments, reformulating includes adding a viscositymodifier. The viscosity modifier may be selected from a group consistingof a drag reducing agent, a polymer cross-linking agent, a polymer andany combination thereof. Reformulating may include adding an aqueousliquid. In some embodiments, the electrodialysis system is configured tooperate with a minimum current density of at least about 50 amps/m² ineach stack. In some embodiments, the diluate is contaminated so as tohave a conductivity of no less than 0.3 Siemens/meter, 1.0Siemens/meter, 3.0 Siemens/meter or 10.0 Siemens/meter.

In accordance with another embodiment of the present disclosure, amethod operates an electrodialysis system. The electrodialysis systemhas at least one stack of at least one pair of electrodes. At least onecell pair having an anion exchange membrane and a cation exchangemembrane is disposed between the at least one part of electrodes. Thesystem is configured to utilize a voltage, applied to the at least onepair of electrodes, of V per cell pair disposed between the at least onepair of electrodes. The system is configured for conventional operationwith a liquid feed having a conductivity below 0.3 Siemens/m.

The method includes providing the liquid feed having a conductivityabove 0.3 Siemens/m, and applying the voltage, of less than about 0.2Vper cell pair, to the at least one pair of electrodes. In variousembodiments, the liquid feed has a conductivity above about 1.0Siemens/m, above about 3.0 Siemens/m, or above about 10.0 Siemens/m. Thevoltage may be less than about 0.15 V or about 0.10 V per cell pair.

In accordance with another embodiment of the present disclosure, anelectrodialysis system includes first and second stacks. Each stack hasat least one pair of electrodes, between which is disposed at least onecell pair having an anion exchange membrane and a cation exchangemembrane. Each of the first and second stacks has a diluate input, adiluate output and a concentrate output. The diluate output of the firststack is fluidly coupled to the diluate input of the second stack.

First and second voltage sources are coupled to the at least one pair ofelectrodes of the first and second stacks respectively so as to apply afirst voltage to the first stack and a second voltage to the secondstack. The first voltage is lower than the second voltage by at leastabout 10%. In various embodiments, first voltage is lower than thesecond voltage by at least about 20% or at least about 50%. In someembodiments, the first voltage is about 0.1 V per cell pair.

The first stack may have a first electrical resistance and the secondstack may have a second electrical resistance. The ratio of the firstvoltage to the second voltage is approximately equal to a square root ofa ratio of the first electrical resistance to the second electricalresistance.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of embodiments will be more readily understood byreference to the following detailed description, taken with reference tothe accompanying drawings, in which:

FIG. 1 depicts a schematic diagram of an exemplary conventional systemthat reuses produced water in a fossil fuel extraction operation;

FIG. 2 depicts a schematic diagram of an exemplary system that reusesproduced water in a fossil fuel extraction operation according to oneembodiment of the present disclosure;

FIG. 3 depicts an exemplary schematic diagram of an electrodialysisstack;

FIG. 4 depicts an exemplary schematic diagram of the operation of theelectrodialysis stack of FIG. 3; and

FIG. 5 depicts an exemplary multi-stack electrodialysis system used topartially desalinate produced water.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Definitions. As used in this description and the accompanying claims,the following terms shall have the meanings indicated, unless thecontext otherwise requires:

“Produced water” means a fluid that returns to the surface after afossil fuel extraction operation. Produced water may include flowbackwater.

“Fossil fuel extraction fluid” means a fluid selected from the groupconsisting of hydraulic fracturing fluid, fluid used in advanced oilrecovery, and a combination thereof.

A “fossil fuel extraction operation” means an operation selected fromthe group consisting of hydraulic fracturing, advanced oil recovery, anda combination thereof.

A liquid is “contaminated” when it contains ionic dissolved solids.

A “voltage source” is an arrangement for supplying a voltage to a load.First and second voltage sources need not be developed from twoindependent circuits, as long as each voltage source provides thevoltage level ascribed to it.

Water use and management incur significant costs for conventional fossilfuel extraction operations. FIG. 1 depicts a conventional system 100 forextracting fossil fuels, in which the extraction fluid generator 105adds viscosity modifiers, such as drag reducing agents, cross-linkingagents, and/or polymers, to at least fresh water 107 to create anextraction fluid 109. The system 100 injects the extraction fluid 109into a well 110. By fracturing the underlying rock formations, theextraction fluid 109 loosens beds of fossil fuels and thereby enablesthe fuels to be more readily harvested. Alternatively, or incombination, in advanced oil recovery, the extraction fluid 109 mayserve to scour oil from sub-surface formations. Water from theextraction fluid 109 returns to the surface as produced water 111, whichthe extraction system 100 collects and sends to its distillation system115. The distillation system 115 distills the produced water 111, andthe extraction fluid generator 105 combines the distilled water 117 withfresh water 107 and further viscosity modifiers to create moreextraction fluid 109 for subsequent operations.

As water from the extraction fluid 109 returns to the surface, the water111 becomes contaminated by dissolving various solids from the ground.As a result, the produced water 111 is saline (e.g., between about 0.1Siemens/m to about 5.0 Siemens/m) and sometimes highly saline (e.g.,over about 5.0 Siemens/m). Because common viscosity modifiers are knownto become less effective when used with higher saline fluids, completelydesalinated water can be relied on for producing effective extractionfluid in a consistent manner. For these reasons, distillation has becomethe preferred treatment for recycling produced water in conventionalfossil fuel extraction systems. Since distillation is also an expensiveprocedure, the distillation system 115 contributes substantially to thecost of fossil fuel extraction. For example, water use and managementmay account for 10-15% of the total cost of operations.

Due to a number of surprising discoveries, embodiments of the presentinvention provide energy efficient and cost effective measures toimprove upon conventional fossil fuel extraction systems. For example,embodiments create effective extraction fluids 109 using fluids withhigher salinity than previously used, which were also obtained usingunconventional methods. Compared to using distillation to completelypurify water, employing electrodialysis to partially desalinate producedwater generates significant savings. These savings can outweigh thedrawbacks of formulating an extraction fluid using a fluid of higherelectrical conductivity. Moreover, when viscosity modifiers exceed thethreshold level of conductivity of the fluid with which they will bemixed, using electrodialysis to reduce the conductivity of the producedwater down to the threshold level can be more cost effective thandistilling the produced water or blending the produced water with alarge amount of fresh water. This finding renders distilled waterunnecessarily pure for use in fossil fuel extraction systems, andembodiments use other, less expensive, desalination treatments tosubstitute for distillation.

In particular, embodiments use electrodialysis to partially desalinateproduced water to a salinity that is still viable for use in fossil fuelextraction operations. For a number of reasons, electrodialysis had notbeen an apparent candidate for treating highly saline fluids. First,electrodialysis was conventionally used to desalinate fluids at muchlower salinity levels than sea water, so its potential advantages fortreating produced water was unknown, untested, and unappreciated.Second, electrodialysis systems normally operate at high voltages.Extrapolating this assumption to high salinity gives the illusion ofhigher energy costs than those that are actually incurred.

Embodiments provide electrodialysis systems, and methods of operatingthe same, that enable fossil fuel extraction operations to replace thedistillation systems 115 with electrodialysis systems 215, as depictedin FIG. 2. In these improved systems, the electrodialysis system 215partially desalinates the produced water 111 to form a diluate 116,which the extraction fluid generator 105 combines with fresh water 107and viscosity modifiers to form extraction fluid 109. Theelectrodialysis system 215 also creates a concentrate 118, which can besent to a disposal well or used as a kill fluid to close a well onceextraction operations have been completed.

To demonstrate how an electrodialysis system 215 functions, an exemplaryelectrodialysis stack 300 is depicted in FIG. 3. The stack 300 includesa pair of electrodes, namely, an anode 305 and a cathode 310. The stack300 also includes at least one cell pair 312, and each cell pair 312includes an anion exchange membrane 315, which only allows anions topass through, and a cation exchange membrane 320, which only allowscations to pass through. In various embodiments, the ion exchangemembranes may be any of the Neosepta CMX, CIMS, CMB, AMX, AHA, ACS, AFN,AFX or ACM membranes, manufactured by Astom Corporation, headquarteredin Tokyo, Japan.

When the stack 300 includes multiple cell pairs 312, the cell pairs 312are arranged so that the anion exchange membranes 315 alternate with thecation exchange membranes 320 in the layers of membranes. Each cell pair312 corresponds to two channels through which fluid may flow. Althoughthree exchange membranes 315, 320 are required to define the twochannels, nevertheless, each cell pair 312 itself includes two exchangemembranes 315, 320. Thus, for any given cell pair 312, an exchangemembrane of an adjacent cell pair 312 provides the third membrane thatbounds the second channel of the given cell pair 312.

In various embodiments, a stack 300 may include various channels, e.g.,up to two thousand (2000) channels, defined by alternating anion 315 andcation 320 exchange membranes. In some embodiments, the exchangemembranes 315, 320 are separated by a constant distance so that thechannels have uniform height. However, the exchange membranes mayalternatively be arranged to form channels of different heights.

The stack 300 includes an inlet 302 that receives the diluate 116, andthe stack 300 divides the diluate 116 to flow through alternate channelsof the cell pairs. The stack 300 receives concentrate 118 through aninlet/outlet 330, which the stack 300 divides to flow through thealternating channels that are not occupied by the diluate 116. In thismanner, when diluate 116 flows through a channel, concentrate 118 flowsthrough the channels immediately above and below the diluate 116, andvice versa. In some embodiments, the channels immediately adjacent tothe anode 305 and cathode 310 contain neither diluate 116 norconcentrate 118.

To operate the electrodialysis stack 300, a voltage source 375 applies avoltage to the electrodes 305 and 310, and in response, ionic dissolvedsolids in the diluate 116 flow through the anion 315 and cation 320exchange membranes into the concentrate 118. As a result, the stack 300at least partially desalinates the diluate 116 while increasing thesalinity of the concentrate 118.

This process is depicted in more detail in FIG. 4. This figure depictsan enlarged view of three channels in the stack 300, and variousfeatures of the stack 300 have been removed for clarity. When voltage isapplied to the electrodes 305 and 310, the anode 305 attracts the anionsin the diluate 116 and concentrate 118. For each channel through whichdiluate 116 flows, the layer closer to the anode 305 is an anionexchange membrane 315. Since anion exchange membranes 315 allow anionsto pass through, anions from the diluate 116 permeate the exchangemembrane 315 to flow into the concentrate 118. However, for each channelthrough which concentrate 118 flows, the layer closer to the anode 305is a cation exchange membrane 320. Although anions in the concentrate118 are attracted to the anode 305, the cation exchange membrane 320prohibits the anions from permeating the membrane 320. Thus, anions flowfrom diluate 116 to concentrate 118, and the cation exchange membranes320 prohibit anions in the concentrate 118 from flowing into the diluate116.

Similarly, for each channel through which diluate 116 flows, the layercloser to the cathode 310 is a cation exchange membrane 320, and foreach channel through which concentrate 118 flows, the layer closer tothe cathode 310 is an anion exchange membrane 315. The cathode 310attracts the cations in the diluate 116 and concentrate 118, but thecation exchange membranes 320 allow cations to flow from the diluate 116into the concentrate 118 while the anion exchange membranes 315 prohibitcations from leaving the concentrate 118.

Multi-stack electrodialysis systems 500 connect stacks 300 in series, asdepicted in FIG. 5. In this system 500, each stack 300 includes theelements described in reference to FIG. 3, namely, a pair of electrodes305 and 310 and at least one cell pair 312 having an anion exchangemembrane 315 and a cation exchange membrane 320. Although thisembodiment of a multi-stack electrodialysis system 500 includes stacks300 with equal numbers of cell pairs 312, in various embodiments, thestacks 300 may have different numbers of layers.

The multi-stack system 500 continuously flows concentrate 118 throughalternate channels of the stacks 300, and the system 500 includesconcentrate inlets 505 and concentrate outlets 510 that are fluidlycoupled to re-circulate the concentrate 118 among the stacks 300. Thefirst stack 300 receives the concentrate 118 through an inlet 505,divides the concentrate 118 to flow through alternate channels,aggregates the concentrate 118 into a single stream at the end of thelayers, and sends the concentrate 118 stream through an outlet 510 thatis fluidly coupled to the inlet 505′ of the next stack 300′. The nextstack 300′ processes the concentrate 118 in a similar manner, and thelast stack 300″ sends the concentrate 118 through an outlet 510″ that isfluidly coupled to the inlet 505 of the first stack 300.

As for the diluate 116, the first stack 300 receives diluate 116 throughthe inlet 302 and divides the diluate 116 to flow through the channelsnot occupied by the concentrate 118 (in some embodiments, the diluateinlet 302 is fluidly coupled to the concentrate inlet 505, therebyforming a bleed stream of fluid from the diluate to the concentrate).The voltage source 375 applies a voltage to the electrodes 305, 310 ofthe first stack 300, and the voltage pulls ionic dissolved solids in thediluate 116 across the anion and cation exchange membranes 315, 320 intothe concentrate 118, thereby at least partially desalinating the diluate116. At the end of each layer, the stack 300 aggregates the channels ofdiluate 116 into a single stream and flows the diluate 116 through anoutlet 308. In the multi-stack system, each outlet 308 of a stack 300 isfluidly coupled to the inlet 302 of the subsequent stack 300. Thus, eachsubsequent stack 300 receives diluate 116 that has been furtherdesalinated by the previous stack 300, and the voltage applied to thestack's electrodes 305, 310 pulls additional ionic dissolved solids inthe diluate 116 across the exchange membranes 315, 320 into theconcentrate 118. The final stack 300 in the system 500 flows the diluate116 through an outlet 308″ that is fluidly coupled to the extractionfluid generator 105 of the fossil fuel extraction operation system.

As previously discussed, conventional electrodialysis systems apply highvoltages to their electrodes 315, 320 to desalinate diluates 116 withrelatively low levels of salinity. For example, electrodialysis systemsare conventionally operated at voltages between about 0.5 V and about1.5 V per cell pair. Moreover, electrodialysis systems areconventionally used to desalinate fluids with conductivity below 0.3Siemens/m and produce a diluate that is below about 0.1 Siemens/m.

Embodiments use electrodialysis systems to remediate highly salinefluids to the saline levels suitable for creating extraction fluid.Thus, although previously unconsidered for such purposes,electrodialysis systems can efficiently operate on fluids withconductivity above 0.3 Siemens/m, or current densities above about 50amp/m². Preferably, electrodialysis systems can be used in a costeffective manner to desalinate fluids with conductivities above about1.0 Siemens/m, about 3.0 Siemens/m, and about 10.0 Siemens/m, althoughfluids of other conductivities over 0.3 Siemens/m may be applied.

Further, although electrodialysis systems are often run at voltages inthe range of about 0.5V-1.5V per cell pair, various embodiments of thepresent invention use lower voltages to remediate highly saline fluids,such as produced water 111, in an effective and cost efficient manner.Without wishing to be bound by theory, highly saline fluids exhibitgreater conductivity due to their higher concentrations of ionicdissolved solids, and as a result, the fluids are more responsive tovoltages applied to the stack electrodes 305, 310. Furthermore, fordiluate salinities above roughly 0.3 Siemens/m, the effects ofconcentration polarization and the limiting current density becomeincreasingly insignificant. In this manner, electrodialysis systemsexhibit a lower cost per unit ionic solids removed, for highly salinefluids.

As a result, electrodialysis stacks 300 can remediate highly salinefluids using voltages that are less than about 0.2 V per cell pair. Invarious embodiments, the voltages may be preferably about 0.15 V percell pair, about 0.10 V per cell pair, or about 0.05 V per cell pair,although any voltage less than 0.2 V per cell pair may be used. Thus,electrodialysis systems 500 can be used in fossil fuel extractionsystems to remediate produced water 111 at lower cost than generallyexpected from such systems.

Furthermore, in multi-stack electrodialysis systems 500, conventionally,the same voltage is applied to each pair of electrodes in each stack300. As discussed above, electrodialysis treats highly saline fluidsmore efficiently than lower saline fluids. However, because each stack300 further decreases the salinity of the diluate 116, the subsequentstacks 300 become less cost efficient for processing the fluid. Sinceelectrodialysis is typically used to desalinate fluids to a high levelof purity (less than 0.1 Siemens/m), the limiting current densitytypically constrains the current density that can be drawn. Becausecapital costs are typically high due to the low current densities thatcan be drawn when desalinating streams of high purity, controlling theratio of the current density to the limiting current density canminimize these costs. For example, the ratio may be controlled to beclose to unity, and in some embodiments, the ratio may be equal orgreater than about 0.50. Applying approximately the same voltage acrossthe electrodes in each stack 300 is a convenient way to achieve aconstant ratio of current density to limiting current density in eachstack 300. However, when conductivity is above about 0.1 Siemens/m, thispractice may become ineffective.

Because the fossil fuel extraction operations can use fluids with higherthan expected salinity levels to produce extraction fluid 109, applyingdifferent voltages to different stacks 300 of the electrodialysis system500 can remediate the produced water 111 while controlling the finallevel of the diluate's 116 salinity, at reduced cost. Thus, the voltagesource 375 can control voltages applied to the stacks to producediluates 116 with salinities greater than or equal to 10.0, 3.0, 1.0,0.3, or 0.1 Siemens/m. Although FIG. 5 depicts a single voltage source375 applying voltages to the stacks 300, in alternate embodiments, thesystem 500 may include multiple voltage sources. For example, each stack300 may be coupled to its own voltage source, or each voltage source mayapply different voltages to each stack 300 in a subset of the stacks300.

In one embodiment, the voltage source 375 applies a voltage of about 0.1V per cell pair to the first stack 300 in a multi-stack electrodialysissystem 500. In some embodiments, the voltage source 375 applies avoltage less than about 0.2 V per cell pair to at least one stack 300,but applies voltages greater than about 0.2 V per cell pair to all ofthe other stacks in the electrodialysis system 500. In some embodiments,the smallest voltage may be applied to the first stack 300 in the system500. Alternatively, the voltage source 375 may apply voltages less thanabout 0.2 V per cell pair to all of the stacks, but the voltages amongthe stacks may vary. In some embodiments, the largest and smallestvoltages applied to the stacks 300 may differ by more than about 1%. Forexample, the largest voltage may be about 5%, about 10%, about 20%,about 25%, or about 50% larger than the smallest voltage.

In electrodialysis systems 500, the voltages for the initial stacks 300may be lower than the voltages for later stacks. In some embodiments,the voltage applied to the first stack 300 is at least about 20% lowerthan the voltage applied to the second stack 300′. In furtherembodiments, the voltage for the first stack 300 is at least about 50%lower. In some embodiments, for each stack 300 in a multi-stack system500, the voltage applied to the stack 300 may be a constant percentagelower than the voltage applied to the subsequent stack 300′. Forexample, the voltage for the first stack 300 may be about 10% lower thanthe voltage for the second stack 300′, which in turn may be about 10%lower than the voltage for the third stack 300″.

In many embodiments, the voltage applied to any given stack 300 in amulti-stack electrodialysis system 500 may be expressed as:

$V_{cp}^{*2} = {\frac{K_{C}}{K_{E}}\left( {{\overset{\_}{r}}_{m} + \frac{2\; h_{d}}{\sigma \; k_{d}} + \frac{2\; h_{c}}{\sigma \; k_{c}}} \right)\frac{1}{\frac{1}{r}\left( {1 - \left( \frac{1}{1 + r} \right)^{T}} \right)}\frac{1}{3.15569\; e\; 7}}$

In this formula, V_(cp)* refers to the voltage per cell pair.

K_(C) is the capital cost of the multi-stack electrodialysis system 500,divided by half of the total surface areas of the anion and cationexchange membranes 315, 320 in the stack. In some embodiments, thesurface area may be expressed in m². In some embodiments, K_(C) may bebetween about 25 and about 150 $/m², and in one embodiment, K_(C) isabout 50 $/m².

K_(E) is the cost of electricity. In some embodiments, the cost may beexpressed as $/Joule. In various embodiments, K_(E) may be between about1.4×10⁻⁸ and about 5.6×10⁻⁸ $/Joule, and in one embodiment, K_(E) may beabout 2.8×10⁻⁸ $/Joule.

r _(m) is the average of the anion and cation membrane electricalresistance measured in a solution of 0.5 M NaCl. The resistance may bemeasured in Ωm². In some embodiments, the resistance may be betweenabout 2.00×10⁻⁴ and about 4.00×10⁻⁴ Ωm², and in one embodiment, theresistance may be about 3.00×10⁻⁴ Ωm². In certain cases, the effectiveresistance may be higher as the spacer may block a portion of themembrane surface.

σ is the spacer shadow factor. Because the spacer reduces the transferof ions across the membranes, the spacer shadow factor corrects diluateand concentrate resistance accordingly. In some embodiments, the spaceris a polymer mesh, situated between an anion exchange membrane and anadjacent cation exchange membrane. In some embodiments, the spacer isporous and designed to disturb the flow of fluid in a way thatfacilitates improved velocity gradients, and hence mass transfergradients, at membrane surfaces. In various embodiments, σ may bebetween about 0.30 and about 0.90. For example, σ may be about 0.50.

h_(d) is the height of a diluate channel. This height may be thedistance between the anion 315 and cation 320 exchange membranes betweenwhich a diluate 116 flows, and the height may be expressed in meters. Invarious embodiments, the height may be between about 0.3 and about 2.5mm (e.g., between about 0.3×10⁻³ m and 2.50×10⁻³ m).

h_(c) is the height of the concentrate channel. This height may be thedistance between the anion 315 and cation 320 exchange membranes betweenwhich a concentrate 118 flows, and the height may be expressed inmeters.

k_(d) and k_(c) are the average diluate conductivity and averageconcentrate conductivity in the stack. The conductivity may be expressedin Siemens/m. In some embodiments, the conductivity of the diluate maybe between about 0.1 and about 30.0 Siemens/m. For example, theconductivity may be about 3.0 or about 4.0 Siemens/m. In variousembodiments, the conductivity of the concentrate may be between about15.0 and about 30.0 Siemens/m.

r is the annual cost of capital, expressed as an interest rate. In manyembodiments, the interest rate may be between about 5-15%, such as 7%.

T is the equipment life in years. In many embodiments, T may be betweenabout 10 years and about 20 years.

In some embodiments, the ratio of the voltage applied to one stack tothe voltage applied to the immediately subsequent stack is equal to asquare root of a ratio of the electrical resistances of the stacks. Invarious embodiments, the ratio of the voltages falls within about 5% ofthe square of the ratio of the electrical resistances. In furtherembodiments, the voltage ratio falls within about 10% of the square ofthe electrical resistances ratio. The electrical resistance of a stackmay be expressed as:

$R_{u} \sim \left( {{2\; r_{m}} + \frac{h}{\sigma \; k_{c}} + \frac{h}{\sigma \; k_{d}}} \right)$

wherein each variable has been described, as above.

Cost advantages of some embodiments of the present invention aredescribed in U.S. Provisional Patent Application No. 61/982,973. Forexample, FIG. 2, on page 9 of the application, depicts an exemplaryelectrodialysis system 500 that includes ten (10) stacks. The feedprovided to the first stack has a conductivity of 0.224 Siemens/m, andvoltages are applied to each stack that halve the conductivity ofdiluate as it flows through that particular stack. FIG. 9, on page 14 ofthe application, depicts the capital and energy costs of each stack inthis system 500. The figure also depicts the total cost of adistillation system to purify a feed with a conductivity of 0.224Siemens/m. Thus, from this figure, one of ordinary skill in the art canappreciate the reduced costs incurred from a multi-stack electrodialysissystem, compared to a distillation system.

In various embodiments, the electrodialysis system 500 may continuerecirculating concentrate until the concentrate reaches a salinity of atleast 150,000 ppm, or a salinity between about 200 g/L and about 400g/L. Then, the extraction system may siphon concentrate from theelectrodialysis system 500 for disposal, or for use in well completion.In some embodiments, the extraction system bleeds out the concentrate ona continuous basis.

The embodiments of the invention described above are intended to bemerely exemplary; numerous variations and modifications will be apparentto those skilled in the art. All such variations and modifications areintended to be within the scope of the present invention as defined inany appended claims.

What is claimed is:
 1. A method of reusing produced water resulting froma fossil fuel extraction operation, the method comprising: providing theproduced water as an input to an electrodialysis system; running theelectrodialysis system to produce a diluate and a concentrate, whereinthe diluate is contaminated so as to have a conductivity of no less than0.1 Siemens/meter; reformulating the diluate to produce fossil fuelextraction fluid; and using the produced fossil fuel extraction fluid inthe fossil fuel extraction operation.
 2. A method of claim 1, whereinreformulating includes adding a viscosity modifier.
 3. A method of claim2, wherein the viscosity modifier is selected from a group consisting ofa drag reducing agent, a polymer cross-linking agent, a polymer and anycombination thereof.
 4. A method of claim 1, wherein reformulatingincludes adding an aqueous liquid.
 5. A method of claim 1, wherein theelectrodialysis system is configured to operate with a minimum currentdensity of at least about 50 amps/m² in each stack.
 6. A method of claim1, wherein the diluate is contaminated so as to have a conductivity ofno less than 0.3 Siemens/meter.
 7. A method of claim 1, wherein thediluate is contaminated so as to have a conductivity of no less than 1.0Siemens/meter.
 8. A method of claim 1, wherein the diluate iscontaminated so as to have a conductivity of no less than 3.0Siemens/meter.
 9. A method of claim 1, wherein the diluate iscontaminated so as to have a conductivity of no less than 10.0Siemens/meter.
 10. A method of operating an electrodialysis systemhaving at least one stack of at least one pair of electrodes, betweenwhich is disposed at least one cell pair having an anion exchangemembrane and a cation exchange membrane, wherein the system isconfigured to utilize a voltage, applied to the at least one pair ofelectrodes, of V per cell pair disposed between the at least one pair ofelectrodes, the system configured for conventional operation with aliquid feed having a conductivity below 0.3 Siemens/m, the methodcomprising: providing the liquid feed having a conductivity above 0.3Siemens/m; and applying the voltage, of less than about 0.2V per cellpair, to the at least one pair of electrodes.
 11. A method of claim 10,wherein the liquid feed has a conductivity above 1.0 Siemens/m.
 12. Amethod of claim 10, wherein the liquid feed has a conductivity above 3.0Siemens/m.
 13. A method of claim 10, wherein the liquid feed has aconductivity above 10.0 Siemens/m.
 14. The method of claim 10, whereinthe voltage is about 0.15 V per cell pair.
 15. The method of claim 10,wherein the voltage is about 0.10 V per cell pair.
 16. Anelectrodialysis system comprising: first and second stacks, each stackhaving at least one pair of electrodes, between which is disposed atleast one cell pair having an anion exchange membrane and a cationexchange membrane; each of the first and second stacks having a diluateinput, a diluate output and a concentrate output, wherein the diluateoutput of the first stack is fluidly coupled to the diluate input of thesecond stack; and first and second voltage sources coupled to the atleast one pair of electrodes of the first and second stacks,respectively, so as to apply a first voltage to the first stack and asecond voltage to the second stack, wherein the first voltage is lowerthan the second voltage, by at least about 10%.
 17. An electrodialysissystem of claim 16, wherein the first stack has a first electricalresistance and the second stack has a second electrical resistance, anda ratio of the first voltage to the second voltage is approximatelyequal to a square root of a ratio of the first electrical resistance tothe second electrical resistance.
 18. An electrodialysis system of claim16, wherein the first voltage is lower than the second voltage by atleast about 20%.
 19. An electrodialysis system of claim 16, wherein thefirst voltage is lower than the second voltage by at least about 50%.20. An electrodialysis system of claim 16, wherein the first voltage isabout 0.1 V per cell pair.